Question: If $x \boxdot y = 3x-4y$ and $x \bigtriangledown y = 4x-y$, find $(1 \bigtriangledown -5) \boxdot -1$.
First, find $1 \bigtriangledown -5$ $ 1 \bigtriangledown -5 = (4)(1)-(-5)$ $ \hphantom{1 \bigtriangledown -5} = 9$ Now, find $9 \boxdot -1$ $ 9 \boxdot -1 = (3)(9)-(4)(-1)$ $ \hphantom{9 \boxdot -1} = 31$.